It is "one and a half hours" because you have more than one hour ( one hour plus half an hour ) hence implying that it is plural and not just a single hour. both "one" and "a half" are describing the noun "hour", so two. the other way that it could be stated is "one hour and a half". the one in this case is the only one describing "hour" and "a half" is also describing "hour" but it wasn't written because the "hour" was implied (understood but not written). if you didn't imply it then it would look like this "one hour and a half hour", but that is just silly sounding. anyway, i hope this clears things up for those of you who didn't understand.

Blatant's explanation is absolutely right. It is "one and a half hours" because it means (one hour) + (half an hour) equals = "one and a half hours" (which means more than one hour). As you know, anything counted more than one is already considered PLURAL, so there's no need to get confused about that.